Gromov invariants of \(S ^{2}\)-bundles over 4-manifolds
type: Item
instance of: scholarly article
title: Gromov invariants of \(S ^{2}\)-bundles over 4-manifolds
zbMATH Open document ID: 1039.53100
DOI: 10.1016/S0166-8641(01)00234-6
published in: Topology and its Applications
publication date: 2003-03-10T00:00:00Z
review text: Given a symplectic \(S^2\)-fibration \(\pi:W\to M\) and homology class \(A\) such that \(\pi(A) \neq 0\), the author develops a relation between the Gromov-Witten invariants of the total space \(W\) of the fibration and those of the base space \(M\). In particular, the author shows that for suitable generic points and fibers, the Gromov-Witten invariants of a lift \(\hat{A}\in H_2(W,\mathbb{Z})\) of a simple class \(A\) are equal to \(2^g\) times the Gromov-Witten invariants of the class \(A\). As a corollary, the author constructs infinitely many deformation classes of symplectic structures on \(W\) when the base \(M\) is a simply connected minimal elliptic surface.
Mathematics Subject Classification ID: 53D45
Mathematics Subject Classification ID: 57R17
zbMATH DE Number: 1879096
zbMATH Keywords: Gromov-Witten invariants
zbMATH Keywords: sphere bundles
zbMATH Keywords: homology
zbMATH Keywords: minimal elliptic surface
author: Haydeé Herrera
reviewed by: Tyler Jarvis
MaRDI profile type: Publication
Wikidata QID: Q125049412
cites work: Q4003026
cites work: Classification of oriented sphere bundles over a 4-complex
cites work: Knots, links, and 4-manifolds
cites work: On genericity for holomorphic curves in four-dimensional almost-complex manifolds
cites work: Gromov invariants and symplectic maps
cites work: The Gromov invariants of Ruan-Tian and Taubes
cites work: Q5663112
cites work: Q3837744
cites work: Examples of symplectic structures
cites work: Corrigenda to: Introduction to Symplectic Topology
cites work: Q4307618
cites work: A mathematical theory of quantum cohomology
cites work: Higher genus symplectic invariants and sigma models coupled with gravity
cites work: Totally geodesic maps
cites work: Classification problems in differential topology. V: On certain 6- manifolds
description: scientific article; zbMATH DE number 1879096